We can calcualte “What is the probability of event A given event B?”" using Bayesian. This is called conditional probablity
Eg: False positive or False negative rates.
Polls : Have you even used dating websites?
US Militray early HIV testing in military
ELISA -sensitivity (true positive): 93% p(+/HIV) = 0.93 -specificity (true negative) : 99% p(-/No HIV) = 0.99
Western blot -sensitivity (true positive): 99.9% -specificity (true negative) : 99.1%
prevalence : 1.48 / 1000 people p(HIV) = 0.0148 which is prior
Bayes-tree
This updating scheme we have here is general property of the Bayesian models
Frequentist: Its relative frequency in large number of trials Bayesian : Probability of an event happening is equated to another event
Confidence Interval : The proportion of random samples of size n from the same population that produce confidence interval that contain the true population parameter.
Credible Interval : We can express the true parameter not as a fixed value but with a probablity This will let us contruct something like a credible intervals expect we can make probabilistic statements about the paramenter falling within that range
RU-486 effective or not? 40 women are divided into two groups with one taking RU 486 and the other standard therapy.4/20 got pregnant where RU 486 used and 16/20 got pregnent where stadard methods are used. How strongly does the data indicate RU 486 is effective? This is a two proportion problem but we can frame it as one proportion test as following: How likely that 4 pregnencies occur in treatment group? p = probability that a given pregnency comes from a treatment group
H\(_{0}\) : p = 0.5 - No difference, pregnency is equally likely to come from the treatment or control group
H\(_{A}\) : p > 0.5 - treatment is more effective, a pregnency is less likely to come from the treatment group
What is likelihood in the Bayes tree? I think it is the sensitivity and specificity of the test.